【摘要】 对时滞控制作用下的参数激励van der Pol-Duffing方程进行了研究,着重研究了时滞参数对该类参数激励系统的1/2亚谐共振-主参数共振分叉响应控制。首先采用摄动法从理论上推导出时滞动力系统的分叉响应方程,再采用数值模拟的方法研究了时滞参数对系统分叉响应的影响。研究结果表明,适当选取时滞参数,不仅可以改变分叉响应曲线的拓扑形态,还可以平移分叉响应曲线,即使其分叉提前或滞后,还能同时满足这两种要求。更多还原

【Abstract】 The van der Pol-Duffing equation,excited under the parameters with two time delays,is studied.The main aim is to study 1/2 subharmonic-primary parametrical resonance bifurcation of this system.Perturbation method is used to obtain the bifurcation equation with time-delays,and numerical method is utilized to analyze the effect of time-delays on the steady state response.The research indicates that 1/2 subharmonic-primary parametrical resonance bifurcation can be well controlled by time-delays feedback.更多还原